Water resources availability, in terms of both quality and quantity, is a very crucial issue in many areas of the world, with small islands being amongst those facing the greatest challenges. In parallel, energy is also a focal point for water supply, since, in many places, it is amongst the main limiting factors for adopting alternative water supply methods. As an example, mature desalination methods with competitive water production costs are not yet widely introduced to Greek islands. This is due to certain characteristics of local electricity grids, such as the very small power reserve margins or the large production cost variation of the available thermal engines, which require additional expenditures for upgrading the energy infrastructure. In this context, it has become obvious that water supply chain problems are inherently linked to the energy quality and availability of an area, leading to the so-called water-energy nexus (WEN) considerations. In that respect, the integrated approach for the solution of water and energy problems has become a topic of increasing attention for the scientific community and for practitioners in the field. With special emphasis on Aegean Sea Islands, i.e. an island region with significant water and energy shortages that jeopardize the local economy development, the present work introduces a framework for applying efficient solutions that integrate water supply with clean energy supply. To that end, the desired island characteristics and critical factors necessary for the successful implementation of the suggested solutions are identified and discussed, while the proposed framework is demonstrated using as case study the small island of Anafi. In more detail, a Linear Programming (LP) model is developed and applied in Anafi island, with results obtained showing that reliable and renewable-based energy and water supply are achievable at feasible cost, contributing at the same time to the considerable reduction of Greenhouse Gases (GHGs). The theoretical modeling framework introduced aims at explaining the path of the research of the integrated water and energy supply for islands from a high-level decision-making perspective; thus not qualifying solutions into the detailed level of implementation (i.e. siting issues and local infrastructure characteristics are not taken into account). (C) 2019 Published by Elsevier Ltd.